Page 44 - Fundamentals of The Finite Element Method for Heat and Fluid Flow

SOME BASIC DISCRETE SYSTEMS
36
T a = 25 °C
2mm 6cm
2
h = 100 W/m K
k = 200 W/mK
8mm 8mm 8mm
8mm
100 °C
Figure 2.16 A heat sink

2
(c) overall heat transfer coefficient U = 600 W/m 2 ◦ C (d) heat exchanger area A = 4m (e)
◦
cold fluid entry temperature T ci = 20 C (f) hot fluid entry temperature T hi = 80 C. Set up
◦
the stiffness matrix and hence solve for the outlet temperature and the effectiveness of the
heat exchanger by using 1 element, 2 elements and 4 elements for the heat exchanger. Also
determine the minimum number of elements required for converged solution.

Exercise 2.5.13 Figure 2.17 shows an arrangement for cooling of an electronic equipment
consisting of a number of printed circuit boards (PCBs) enclosed in a box. Air is forced
through the box by a fan. Select a typical element and write down the stiffness matrix and
show that this method can take care of non-uniform flow (by using the methodology similar
to that in Exercise 2.5.9, the non-uniform flow in each channel can be determined) and
non-uniform heat generation in individual PCB.

Air out

PCB with heat-generating
electronic components

Air in
Figure 2.17 Assembly of printed circuit boards